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Find three distinct integers such that all pairwise sums are powers of 2. Question
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Find three different integers A, B and C such that A+B, A+C and B+C are all powers of 2.
Clarifications:
A, B and C can be negative, zero or positive.
Powers of 2 are: 1, 2, 4, 8, 16, ...
1 answer
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Works for me
The following users marked this post as Works for me:
| User | Comment | Date |
|---|---|---|
| will.octagon.gibson | (no comment) | Jun 22, 2026 at 17:52 |
If we suppose
A+B=2, A+C=4, B+C=8then
Gaussian elimination gives A=-1, B=3, C=5.The only restriction
(other than the obvious observation that the sums must also be distinct) is that the sums must all be even. Perhaps the intention was that people would assume that any solution can be divided down to a case when the smallest sum is 1 and would then conclude that it is unsolvable?
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