MathDB

3

Part of 2016 Iran Team Selection Test

Problems(1)

Iran Team Selection Test 2016

Source: TST 3,day 1,P 3

7/15/2016
Let p≠13p \neq 13 be a prime number of the form 8k+58k+5 such that 3939 is a quadratic non-residue modulo pp. Prove that the equation x14+x24+x34+x44≡0(modp)x_1^4+x_2^4+x_3^4+x_4^4 \equiv 0 \pmod p has a solution in integers such that p∤x1x2x3x4p\nmid x_1x_2x_3x_4.
number theoryprime numbersmodular arithmeticQuadratic Residues