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

Source: Macedonia JBMO TST 2017, Problem 1

June 26, 2018
number theoryprime numbersDivisibility

Problem Statement

Let pp be a prime number such that 3p+103p+10 is a sum of squares of six consecutive positive integers. Prove that pāˆ’7p-7 is divisible by 3636.
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