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Grade: 10
        
What is common factor of 13^7+11^7 and 13^5+11^5..
a)13^5+11^5
b)24
c)49
d)13^2+11^2
 
8 months ago

Answers : (1)

Arun
13827 Points
							
Dear student
 
 
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). 
 
 
Regards
Arun (askIITians forum expert)
8 months ago
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