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# when 6^83+8^83 is divided by 49 , tell the remainder left where ^ denotes raised to?

Swapnil Saxena
102 Points
9 years ago

Express this equation as

(7-1)89 + (7+1)89.

This will give

= (89C0789-89C1788+89C2787+...-89C8772+89C8871-89C8970)+(89C0789+89C1788+89C2787+...-89C8772+89C8871-89C8970)

=2*(89C0789+89C2787+89C4785+...+89C8673+89C8871)

89C0789+89C2787+89C4785+...+89C8673 will all be divisible by 49 because they consist of 72 as one of their factor but not 2(89C8871)

Then 2(89C8871)%49 = 21 ---Remainder

Swapnil Saxena
102 Points
9 years ago

sorry for my mistake, its (7-1)83 + (7+1)83 not (7-1)89 + (7+1)89.

In similar ways of my prev reply  the remainder will be  2(83C8271)%49 =35