1982 USAMO Problems/Problem 4
Problem
Prove that there exists a positive integer such that is composite for every integer .
Solution
Indeed, has the requisite property.
To see why, consider the primes , and observe that
Moreover,
We conclude that
And so the relevant values will, in fact, always be composite.
See Also
1982 USAMO (Problems • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 | ||
All USAMO Problems and Solutions |
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