Need help for Discrete Math problem Thank youSolution8 a mod

Need help for Discrete Math problem. Thank you.

Solution

(8)

a mod 11 =6 or a= 11p+6

b mod 11 =5 or b= 11q+5

ab= (11p+6)(11q+5)

= 11p*11q+11p*5+6*11q+30

=11(11pq+5p+6q)+30

= 11(11pq+5p+6q)+11*2+8

=11(11pq+5p+6q+2)+8

= 11k+8

so, ab= 11k+8

or, ab mod 11= 8