41

Number Theory Level 3

T 2 − K 2 = 41 T^2 - K^2= 41 , O = T × K O = T\times K , what is the sum of all positive factors of O O ?


The answer is 1344.

Dan Shin by Dan Shin , 21, USA

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1 solution

I am assuming that T and K are both positive integers. T 2 − K 2 = 41 ⇒ ( T + K ) ( T − K ) = 41 T^2 - K^2= 41\Rightarrow(T+K)(T-K)=41 . Since 41 is prime, and T − K < T + K T-K<T+K , we get T − K = 1 T-K=1 , T + K = 41 T+K=41 . Solving, we get T = 21 T=21 , K = 20 K=20 .

Thus, O = 420 O=420 and the sum of factors is therefore 1344.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Even if O O is negative, technically the answer should be the same

Arulx Z - 5 years, 4 months ago

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