1979 IMO Problems/Problem 1
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Problem
If and are natural numbers so thatprove that is divisible with .
Solution
We first write Now, observe that and similarly and , and so on. We see that the original equation becomes where and are two integers. Finally consider , and observe that because is a prime, it follows that . Hence we deduce that is divisible with .
The above solution was posted and copyrighted by Solumilkyu. The original thread for this problem can be found here: [1]
See Also
1979 IMO (Problems) • Resources | ||
Preceded by First question |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
All IMO Problems and Solutions |