Euler's Theorenm and Remainder problems.

Hello! I am Harsh Sharma B.Tech in Computer Science CAT 2016-98 percentile (OA) Aptitude Trainer/Tutor = Movies | Music | Football 2

1. Euler Number Let's start with first understanding the basic concepts of Euler Number.

4L The Euler number of a natural number x means the number of natural numbers which are less than x and are co-prime to x. E.g. The Euler number of 6 will be 2 as the natural numbers 1 & 5 are the only two numbers which are less than 6 and are also co-prime to 6. 4

Example Find Euler Number of 15? Solution - The natural numbers which are less than 15 and are also co-prime to 15 are:- 1,2,4,7,8,11,13,14 So, Euler Number f 15 = 8 5

Formula Mathematically, the Euler number of a number Z denoted by the symbol E(Z) is calculated as explained below E(Z) = Z(1-1/P) (1-1/Q) (1-1/R) where P, Q and R are the different prime factors of Z.

Question- Find Euler Number of 72? 21 2 236 218 E(+z) = 72( 1-2)/ 1-3 7

Example Find Euler Number of 15? Solution-> 15=3*5 So, E(15) = 15(1-1/3) (1-15) -15(2/3) (4/5)

Example Find Euler Number of 19? Solution-> 19=1+19 So, E(19) = 19(1-1/19) - 19(18/19) = 18

Since for a number p' to be prime, the necessary condition is that it should not be divisible by any number other then 1 and itself. So, As a general rule of thumb we can state that Euler number of a prime number will involve all the natural numbers less then it. Hence, Euler Number(prime:p')=p-1 Example->E(13)=12, E(17-16, E(19)=18 and so on. 10

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Harsh Sharma

B.Tech in Computer Science | CAT 2016 - 98.6 percentile (100 percentile in Quants) | Footballer

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Ashish

5 months ago

THANK YOU SIR..

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Niharika Singh

a year ago

The way you explain things is just amazing Sir. We always look forward to your lessons:)

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Babli TIRKEY

a year ago

thank you very much sir

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Harsh Sharma

a year ago

Hi Babli, Thank you for the appreciation. Do watch my other courses too :)

Yash tarekar

a year ago

very easy explanations sir thanku so much

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Harsh Sharma

a year ago

Thank you so much..Keep Sharing Keep Learning :)

Pariwesh Chettri

a year ago

beautifully explained thank you sir....

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Harsh Sharma

a year ago

Thank you so much..Keep Sharing, Keep Learning :)