12

Part of 2014 Ukraine Team Selection Test

Problems(1)

no of pos. integers n suh that p | n! +1 is <= cp^{2/3}

Source: Ukraine TST 2014 p12

Prove that for an arbitrary prime

p \ge 3

the number of positive integers

n

p | n! +1

does not exceed

cp^{2/3}

, where c is a constant that does not depend on

p

primenumber theoryDivisibility