MathDB

n_{1},\ldots ,n_{k}, a

are integers that satisfies the above conditions A)For every

i\neq j

(n_{i}, n_{j})=1

B)For every

i, a^{n_{i}}\equiv 1 (mod n_{i})

C)For every

i, X^{a-1}\equiv 0(mod n_{i})

. Prove that

a^{x}\equiv 1(mod x)

congruence has at least

2^{k+1}-2

solutions. (

x>1

)

Problem Statement