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Yet another divisibility

Source: Indian RMO 1998 Problem 2

October 26, 2005
modular arithmeticnumber theoryprime numbers

Problem Statement

Let nn be a positive integer and p1,p2,p3,…pnp_1, p_2, p_3, \ldots p_n be nn prime numbers all larger than 55 such that 66 divides p12+p22+p32+⋯pn2p_1 ^2 + p_2 ^2 + p_3 ^2 + \cdots p_n ^2. prove that 66 divides nn.
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