The product of any pair of twin primes, when increased by 1, always gives a perfect square.

(2) Let γ be the Euler Gamma,

γ = lim _{n -> ∞} ( Sum _{k = 1...n} 1/k – log n ) = 0.5772156649...

Prove or disprove:

π^{ log γ} = γ^{ log π}

(3) Prove or disprove:

1 + 2 = 3

1*2 + 2*3 + 3*4 = 4*5

1*2*3 + 2*3*4 + 3*4*5 + 4*5*6 = 5*6*7

etc.

(4) 2 2 2 3 2 2 4 2 3 ?

(5) Compute 1/49 to 12 digits, *in your head.*

(6) Name two famous mathematicians whose names are synonymous.

Bonus true story:

Grading papers in a graph-theory course. Problem: prove that if G is not connected, then the complement of G is connected.

"We use a contrapositive proof..."

© 1985-2011, S.E.

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