if m and n are divided by 4 then 2 and 3 are respectively the remainders find the remainder when m square + n square is divided by 4

Asked by dash.ak35 | 8th Apr, 2020, 01:19: PM

Expert Answer:

When m and n are divided by 4, then 2 and 3 are the remainders respectively.
Therefore, m = 4a + 2  and  n = 4b + 3
m2 + n2 = (4a + 2)2 + (4b + 3)2 = 16a2 + 16a + 4 + 16b2 + 24b + 9 = 4(4a2 + 4a + 1 + 4b2 + 6b) + 9 
When m2 + n2 is divided by 4, the remainder will be 9.

Answered by Renu Varma | 8th Apr, 2020, 01:45: PM