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(a+1)^b-1 is divisible by a^{n+1} when b is divisible by a^n

Source: Eotvos 1932 p1

September 10, 2024

number theorydivisible

Problem Statement

Let

a, b

and

n

be positive integers such that

b

is divisible by

a^n

. Prove that

(a+1)^b-1

is divisible by

a^{n+1}