# elementary Number Theory

• Mar 25th 2008, 08:42 PM
elole2009
elementary Number Theory
1-for what values of a(mod 78) will ax is congruence to 26(mod 78) have exactly 13 solutions

2- given 36x ≡ 42 (mod 42) and 4x ≡ 6 (mod 18
a) determine the number of solutions to each coungruence equation.
b) Find integer solutions to each congruence equation
• Mar 25th 2008, 08:45 PM
ThePerfectHacker
Quote:

Originally Posted by elole2009
for what values of a(mod 78) will ax is congruence to 26(mod 78) have exactly 13 solutions

Given $ax\equiv 26(\bmod 78)$ let $d=\gcd(a,26)$. It $d|26$ then there shall be exactly $d$ solutions mod 78. Thus, what are those values of $a$?