1

Part of 2017 Macedonia JBMO TST

Problems(1)

3p+10 is a sum of six consecutive positive integers => 36 | p-7

Source: Macedonia JBMO TST 2017, Problem 1

p

be a prime number such that

3p+10

is a sum of squares of six consecutive positive integers. Prove that

p-7

is divisible by

36

number theoryprime numbersDivisibility