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Math Help - Find all primes p

  1. #1
    MHF Contributor alexmahone's Avatar
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    Find all primes p

    Find all primes p such that 4p^2 + 1 and 6p^2 + 1 are both primes.
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    Opalg's Avatar
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    Quote Originally Posted by alexmahone View Post
    Find all primes p such that 4p^2 + 1 and 6p^2 + 1 are both primes.
    Hint: Work mod 10. In other words, think about the final digit of p. Every prime number apart from 2 and 5 ends with 1, 3, 7 or 9. What does that tell you about 4p^2 + 1 and 6p^2 + 1?
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by Opalg View Post
    Hint: Work mod 10. In other words, think about the final digit of p. Every prime number apart from 2 and 5 ends with 1, 3, 7 or 9. What does that tell you about 4p^2 + 1 and 6p^2 + 1?
    It tells me that for every prime p apart from 2 and 5, either 4p^2 + 1 or 6p^2 + 1 is divisible by 5.
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