Question

If If K1,K2,K3.........Kn Are Odd Natural No.Then The Remainder When K1 ^2+K2^2+.....Kn^2 Is Divided By 4 Is Always Equal To What ?

Answer 1

Answer:

n

Step-by-step explanation:

If If K1,K2,K3.........Kn Are Odd Natural No.Then The Remainder When K1 ^2+K2^2+.....Kn^2 Is Divided By 4 Is Always Equal To What ?

K1 , K2 , K3 , K4 , ..........Kn are odd numbers

=> Kn = (2n + 1)

=>  Kn² = (2n+1)²

=> Kn² = 4n² + 1 + 4n

=> Kn² = 4n(n+1) + 1

So Kn² divided by 4 leave remainder = 1

Similarity k1² to  kn²  each will remainder = 1

so remainder will be n

Final Remainder will depend upon value of n

for  n = 4m , 4m+1  , 4m+2 & 4m+3  Remainder will be respectively 0 , 1 , 2 & 3