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when 6^83+8^83 is divided by 49 , tell the remainder left where ^ denotes raised to? PLS EXPLAIN (Acco. to me its 0)......

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


PLS EXPLAIN (Acco. to me its 0)......


 

Grade:9

1 Answers

himanshu panwar
30 Points
9 years ago

we can write this question as

(7-1)89 + (7+1)89.  

open this binomially

=  ( 89C0789 89C1788 89C2787 +... - 89C87789C88789C8970) + (89C0789 89C1788 89C2787 + ...- 89C87789C88789C8970)

=2*( 89C0789 89C2787 89C4785 +...89C867389C8871)

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

so  dividing this 2(89C8871) by 49

we get   2(89C8871)%49 = 21 ---Remainder

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