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Math · Advanced Math
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Theorem 2.29 The congruence f(x) 0 (mod p) of degree n, with leading coefficient an- 1, has n solutions if and only if f(x) is a factor of xP -x modulo p , that is, if and only if xp--/(x)q(x) + ps(x), where q(x) and s(x) have integral coefficients, q(x) has degree p - n and leading coefficient 1, and where either s(x) is a polynomial of degree less than n or s(x) is zero
2. Prove that 2x3 + 5x2 + 6x + 10 (mod 7) has three solutions by use of Theorem 2.29.
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