A number theory problem by Paola Ramírez

Number Theory Level 1

If m m and n n are positive integers so that m n + m n + 1 + m n + 2 = 39 m^{n}+m^{n+1}+m^{n+2}=39 , find n m n^m


The answer is 1.

Paola Ramírez by Paola Ramírez , 24, Mexico

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2 solutions

Paola Ramírez
Jul 17, 2015

m n ( 1 + m + m 2 ) = m n + m n + 1 + m n + 2 = 39 ⇒ m n m^n(1+m+m^2)=m^{n}+m^{n+1}+m^{n+2}=39\Rightarrow m^n is a prime factor of 39 : 1 , 3 , 13 , 39 39:1,3,13,39

After trying with all cases , only m = 3 m=3 and n = 1 n=1 meets ∴ n m = 1 \therefore n^m=1

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohit Gupta
Jul 17, 2015

Well great method .. but still the ques is easily done through assumptioms:-)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I too did it in 5 minutes by assumption.

Anuj Shikarkhane - 5 years, 11 months ago

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