Proving Divisibility #1

Number Theory Level 2

Is 43 101 + 17 101 { 43 }^{ 101 }+{ 17 }^{ 101 } divisible by 43 + 17 43+17 ?

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Maninder Dhanauta by Maninder Dhanauta , 22, Canada

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1 solution

x n + y n = ( x + y ) ( x n − 1 − x n − 2 y + x n − 3 y 2 − . . . + x n − n y n − 1 ) x^n+y^n=(x+y)(x^{n-1} - x^{n-2}y + x^{n-3}y^2 -... +x^{n-n}y^{n-1} ) for odd n ∈ N n\in\mathbb{N} . Taking x = 43 , y = 17 , n = 101 x=43,y=17,n=101 we get the result.

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