What is the Common factor of (13^7+11^7) and (13^5+11^5)
Riya singh , 5 Years ago
Grade 12
Algebra> What is the Common factor of (13^7+11^7) ...
1 Answers
Arun
Last Activity: 5 Years ago
For n odd, we have the algebraic identities
x^n + y^n = (x + y)(x^(n-1) - x^(n-2)y + x^(n-3)y^2 + ... + x^2 y^(n-3) - xy^(n-2) + y^(n-1)).
Therefore,
13^7 + 11^7 = (13 + 11)(13^6 - 13^5*11 + 13^4*11^2 - 13^3*11^3 + 13^2*11^4 - 13*11^5 + 11^6)
13^5 + 11^5 = (13 + 11)(13^4 - 13^3*11 + 13^2*11^2 - 13*11^3 + 11^4)
and it follows that 24 is a common factor of (13^7 + 11^7) and (13^5 + 11^5).
Provide a better Answer & Earn Cool Goodies
Enter text here...
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
Enter text here...
Other Related Questions on Algebra
Can we divide two vectors? If this is possible then how?
Algebra
1 Answer Available
Last Activity: 10 Month ago(s)
How do you write “the product of 18 and q” as an algebraic expression?
Algebra
1 Answer Available
Last Activity: 10 Month ago(s)
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
Algebra
0 Answer Available
Last Activity: 1 Year ago(s)