Mathematics, 02.11.2019 03:31 Milanchik28
Find the solutions of the congruence 15x^2 + 19x = 5 (mod 11). [hint: show the congruence is equivalent to the congruence 15x^2 + 19x + 6 = 0 (mod 11). factor the left-hand side of the congruence; show that a solution of the quadratic congruence is a solution of on eof hte two different linear congruences.]
it was easy to follow the hint of adding 6 to both sides and factoring the left-hand side, but to solve the congruences, i didn't know how. the solution manual says that the inverse of 5 modulus 11 is 9, and multiplying both sides of 5x + 3 = 0 (mod 11) by 9 yeilds x + 27 = 0 (mod 11), so x = -27 = 6 (mod 11). similarly, an inverse of 3 modulo 11 is 4, and we get x = -8 = 3 (mod 11). so the solution set is {3, 6} (and anything congruenct to these modulo 11).
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Mathematics, 22.06.2019 00:30
The nth term of a sequence in 2n-1 the nth term of a different sequence is 3n+1 work out 3 numbers that are in bothe sequences and are between 20 and 40
Answers: 2
Find the solutions of the congruence 15x^2 + 19x = 5 (mod 11). [hint: show the congruence is equiva...
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