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

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

Question

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

adithya swaroop · Answer

I think answer is 2

procedure:

6^83+8^83/49 can also be written as (7-1)^83+(7+1)^83/49

now apply binomial theorem

(x+1)^n=nC0+nC1(x)+nC2(x^2)...................

(x-1)^n=nC0-nC1(x)+nC2(x^2)............

after applying we get 2(83C0)+2(83C2(7^2)+83C4(7^4)...........)/49

we can observe that every number in the second part is divisible by 49 where as first part cant.therefore i.e the remainder i.e 2

To get more clarity refer this eg:625+4/25 remainder? ans 4

pranjal shukla · Answer

ANS)1.84617489 &times; 1073

Sathya · Answer

(7-1) 89 + (7+1) 89 . This will give = ( 89 C 0 7 89 - 89 C 1 7 88 + 89 C 2 7 87 + ... - 89 C 87 7 2 + 89 C 88 7 1 - 89 C 89 7 0 )+( 89 C 0 7 89 + 89 C 1 7 88 + 89 C 2 7 87 + ... - 89 C 87 7 2 + 89 C 88 7 1 - 89 C 89 7 0 ) =2*( 89 C 0 7 89 + 89 C 2 7 87 + 89 C 4 7 85 + ... + 89 C 86 7 3 + 89 C 88 7 1 ) 89 C 0 7 89 + 89 C 2 7 87 + 89 C 4 7 85 + ... + 89 C 86 7 3 will all be divisible by 49 because they consist of 7 2 as one of their factor but not 2( 89 C 88 7 1 ) Then 2( 89 C 88 7 1 )%49 = 21 ---Remainder

Sathya · Answer

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( 83 C 82 7 1 )%49 =35

Manoj gupta · Answer

What this %49 means ,I am not able to understand it ,please clarify it to me. Otherwise your answer is perfecg

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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)......

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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)......

5 Answers

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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)......