Difference between revisions of "1973 AHSME Problems/Problem 3"
Rockmanex3 (talk | contribs) (Solution to Problem 3) |
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[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] |
Revision as of 12:56, 20 February 2020
Problem
The stronger Goldbach conjecture states that any even integer greater than 7 can be written as the sum of two different prime numbers. For such representations of the even number 126, the largest possible difference between the two primes is
Solutions
We can guess and check small primes, subtract it from , and see if the result is a prime because the further away the two numbers are, the greater the difference will be. Since , we can eliminate , , and as an option because subtracting these would result in a composite number.
If we subtract , then the resulting number is , which is not prime. If we subtract , then the resulting number is , which is also not prime. But when we subtract , the resulting number is , a prime number. The largest possible difference is .
See Also
1973 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 | ||
All AHSME Problems and Solutions |