52009+132009÷8 Find the remainder Please tell the process
52009+132009÷8
Find the remainder
Please tell the process
Manish soni , 6 Years ago
Grade 10
10 grade maths> 5 2009 +13 2009 ÷8 Find the remainder Ple...
2 Answers
Arun
Last Activity: 6 Years ago
Here, we have 5^2009 + 13^2009
We know that a^n + b^n is always divisible by (a+b) when n is odd.
2009 is an odd number.
So, 5^2009 + 13^2009 is divisible by (5+13) i.e 18.
Hence, the remainder is 0.
We know that a^n + b^n is always divisible by (a+b) when n is odd.
2009 is an odd number.
So, 5^2009 + 13^2009 is divisible by (5+13) i.e 18.
Hence, the remainder is 0.
Aditya Gupta
Last Activity: 6 Years ago
Actually 5^2009= 5*25^1004
Note that 25=8*3+1
Since remainder of 25^n when divided by 8 is 1, so remainder when 5^2009 divided by 8 is 5
Now 13^2009=13*169^1004
But 169= 8*21+1
So remainder when 13^2009 is divided by 8 is 13*1 or 13-8= 5
So net remainder is 5+5=10 or 10-8
=2
Provide a better Answer & Earn Cool Goodies
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Other Related Questions on 10 grade maths
What are the advantages and disadvantages of mean, median and mode?
What are the advantages and disadvantages of mean, median and mode?
10 grade maths
1 Answer Available
Last Activity: 1 Year ago
Find the sum of the first 100 natural numbers.
Find the sum of the first 100 natural numbers.
10 grade maths
1 Answer Available
Last Activity: 3 Years ago
AOBC is a rectangle whose three vertices are A(0,-3), O(0,0) and B (4,0). The length of its diagonal is__
AOBC is a rectangle whose three vertices are A(0,-3), O(0,0) and B (4,0). The length of its diagonal is__
10 grade maths
1 Answer Available
Last Activity: 3 Years ago
For an AP, it is given that first term (a)= 5 and Common Difference (d) = 3 and nth term = 50. Find n and sum of first n terms of AP
For an AP, it is given that first term (a)= 5 and Common Difference (d) = 3 and nth term = 50. Find n and sum of first n terms of AP
10 grade maths
1 Answer Available
Last Activity: 3 Years ago
The value(s) of k for which the quadratic equation 2x^2 + kx + 2 = 0 has equal roots, is (a) 4 (b) pm 4 (c) -4 (d) 0
The value(s) of k for which the quadratic equation 2x^2 + kx + 2 = 0 has equal roots, is (a) 4 (b) pm 4 (c) -4 (d) 0
10 grade maths
1 Answer Available
Last Activity: 3 Years ago