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

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

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

Think You Can Provide A Better Answer ?

Other Related Questions on Magical Mathematics[Interesting Approach]

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

IIT JEE Courses

One Year IIT Programme

Two Year IIT Programme

Crash Course

NEET Courses

One Year NEET Programme

Two Year NEET Programme

One to One

School Board

Live Online classes

Class 11 & 12

Class 9 & 10

Class 6, 7 & 8

Test Series

JEE test series

NEET test series

C.B.S.E test series

Complete Self Study Packages

FULL COURSE

For class 12th

For class 11th

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

Think You Can Provide A Better Answer ?

Other Related Questions on Magical Mathematics[Interesting Approach]

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

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

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