Question

The remainder when aa is divided by 77 is 22 and the remainder when bb is divided by 77 is 55. (so a mod 7=2a mod 7=2, b mod 7=5b mod 7=5) find: (a+a) mod 7(a+a) mod 7 equation editor equation editor (a+b) mod 7(a+b) mod 7 equation editor equation editor (3a) mod 7(3a) mod 7 equation editorequation editor (2b) mod 7(2b) mod 7

Answer 1

$a\equiv2\pmod7$
$b\equiv5\pmod7$

$a+a\equiv2+2\equiv4\pmod7$

$a+b\equiv2+5\equiv7\equiv0\pmod7$

$3a\equiv6\pmod7$

$2b\equiv10\equiv3\pmod7$