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Two to the Tee (Posted on 2005-07-29) Difficulty: 3 of 5
Prove that 2T-3U=1 has only two integer solutions: T=1 and U=0, and T=2 and U=1.

See The Solution Submitted by Old Original Oskar!    
Rating: 4.0000 (4 votes)

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U > 1 impossible | Comment 2 of 5 |
2T-3U=1 means 2T-1+2T-2+...+2+1=2T-1=3U = 2U+...+2U+1 where the binomial theorem has been employed to get the last expression. But

2T-1+2T-2+...+2+1=2U+...+2U+1

is impossible for U>1 since there will be a gap in the powers of 2 being summed on the rhs while no such gap appears in the powers of 2 being summed on the lhs, although I cannot yet give a rigorous proof.

Edited on July 29, 2005, 9:04 pm
  Posted by Richard on 2005-07-29 20:56:26

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