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P10 [Number Theory] - Turkish NMO 1st Round - 2003

Source:

May 14, 2014
modular arithmeticgeometry3D geometryalgebrafactorizationsum of cubes

Problem Statement

Which of the followings is congruent (in  mod 25\bmod{25}) to the sum in of integers 0≤x<250\leq x < 25 such that x3+3x2−2x+4≡0(mod25)x^3+3x^2-2x+4 \equiv 0 \pmod{25}?
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 17<spanclass=′latex−bold′>(D)</span> 22<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 17 \qquad<span class='latex-bold'>(D)</span>\ 22 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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