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Comb(k,2) (Posted on 2018-03-29) Difficulty: 3 of 5
For which k ≥ 3 is k(k-1)/2 (i.e. k choose 2) one more than a power of a prime number?

No Solution Yet Submitted by Ady TZIDON    
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A few easy ones | Comment 1 of 4
k=3, 3=2^1+1
k=4, 6=5^1+1
k=5, 10=3^2+1
k=8, 28=3^3+1

k(k-1)/2=p^n+1
k^2-k-2p^n-2=0
quadratic formula
k=.5+.5sqrt(9+8p^n)

I just checked primes up to 100 and powers that kept the discriminant small enough to see whether the square root had a decimal on my calculator.  So there may be larger solutions, but if so they are pretty big (or n=1 and p>100).


  Posted by Jer on 2018-03-29 09:29:35
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