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Interesting Problems in Number Theory
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Interesting Problems in Number Theory

## Nilanjan Dutta is teaching live on Unacademy Plus

Nilanjan Dutta
Hi, I am a CAT 100 Percentiler with 100 in DI-LR & 99.9 in Quants. Subscribe to CAT Live Classes with 'NILANJANDUTTA' discount code.

U
7 months ago
Okk
Kaviya mohan
7 months ago
thank u
so much of guess work and doing from example.....it will be so tough for me to attempt in actual exam ,😅
why fake accent sir? Be natural.
not able to understand anything 😔
1. Numbers, Factors, HCF & LCM (Interesting Problems in Number Theory) By Nilanjan Dutta CAT 100%-iler CAT Preparation with 100 Percentilers

2. Brief Introduction About Myself BESU Shibpur, 2012 pass-out (CS) > Final Year (2011 - 12 season) appeared for CAT/XAT IIFT > CAT 99.43, XAT 99.35, lIFT 99.59 Converts - XLRI, IIM-Indore, IIFT XLRI 2014 pass-out CAT 100%-iler > Working as a Business Consultant with an IT firm in Kolkata QA-DI-LR & GD-Pl Mentor 2nd attempt at CAT-100%-ile in CAT 2016 > National Level Debater, Lead Actor, Sports Enthusiast

3. Numbers, Factors, HCF & LCN IMS SIMCAT 2018 A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc is: IS: A prime number Divisible by 7 Fifth power of an integer Cube of an integer

4. Numbers, Factors, HCF & LCN IMS SIMCAT 2018 A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc' is: A prime number Divisible by 7 Fifth power of an integer Cube of an integer sum of the squares of"b' & c'-> Perfect Square

5. Numbers, Factors, HCF & LCN IMS SIMCAT 201a A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc' is: A prime number Divisible by 7 Fifth power of an integer Cube of an integer Sum of the squares of 'b' & 'c' -> Perfect Square (3, 4, 5) or (6, 8, 10) Pythagorean Triplets

6. Numbers, Factors, HCF & LCN IMS SIMCAT 2018 A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc' is: A prime number Divisible by 7 Fifth power of an integer Cube of an integer Sum of the squares of 'b' & 'c' -> Perfect Square (3, 4, 5) or (6, 8, 10) 'c' is odd (three digit odd number)

7. Numbers, Factors, HCF & LCN IMS SIMCAT 2018 A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc' is: A prime number Divisible by 7 Fifth power of an integer Cube of an integer Sum of the squares of 'b' & 'c' -> Perfect Square "c' is odd (three digit odd number) c 3, b 4

8. Numbers, Factors, HCF & LCN IMS SIMCAT 2018 A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc' is: A prime number Divisible by 7 Fifth power of an integer Cube of an integer Sum of the squares of 'b' & 'c -> Perfect Square "c' is odd (three digit odd number) c 3, b 4 'a' & 'c' are consecutive integers

9. Numbers, Factors, HCF & LCN IMS SIMCAT 2018 A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc' is: A prime number Divisible by 7 Fifth power of an integer Cube of an integer Sum of the squares of 'b' & 'c' ->Perfect Square 'c' is odd (three digit odd number) c 3, b 4 'a' & 'c' are consecutive integers a2/4

10. Numbers, Factors, HCF & LCN IMS SIMCAT 2018 A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc' is: A prime number Divisible by 7 Fifth power of an integer Cube of an integer Sum of the squares of 'b' & 'c' -> Perfect Square 'c' is odd (three digit odd number) c 3, b 4 'a & 'c' are consecutive integers a 2/4 'ab' +1-> Perfect Square

11. Numbers, Factors, HCF & LCN IMS SIMCAT 2018 A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc' is: A prime number Divisible by 7 Fifth power of an integer Cube of an integer sum of the squares of"b, & c'-> Perfect Square 'c' is odd (three digit odd number) c 3, b 4 'a' & 'c' are consecutive integers a 2/4 ab'+ 1 -> Perfect Square 'ab' 24 a 2, b 4, c 3

12. Numbers, Factors, HCF & LCN IMS SIMCAT 2018 A three digit odd number 'abc' has digits a, b and c (all non-zero) in the hundred's, ten's and unit's places respectively. The first and the third digits (i.e. a and c) are consecutive integers. Sum of the squares of the second and the third digits is a perfect square. Similarly one more than the number formed by the first two digits (i.e. the two digit number 'ab') is also a perfect square. The number 'abc' is: sum of the squares of"b, & C-> Perfect Square c' is odd (three digit odd number) A prime number Divisible by 7 Fifth power of an integer Cube of an integer 'a' & 'c' are consecutive integers a 2/4 'ab + 1 -> Perfect Square 'ab' 24 a 2, b 4, c 3 'abc 243 (35)

13. Thank You!!!! Happy Learning)