Decide whether the congruence statement is true or false 7 2

Decide whether the congruence statement is true or false.

7 29 (mod 11)

Solution

we need to decide that whether congruence statement is true or false

we know that a b (mod c) means a = b + kc where a,b,c,k are some integers.

It simply means that a is remainder when b is divided by k

we have,

7 29 (mod 11)

we can write,

7 = 29 + 11k

if we take take = -2 we have 7 = 29 - 22 = 7

or we can say that 7 is remainder when 29 is divided by 11

So statement is true

Hence we can say that given congruence 7 29 (mod 11) is true.