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| Take Biquadratic, Get Prime (Posted on 2007-06-10) |
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Determine all possible positive primes m such that 7m4 – 3942 is a positive prime number.
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Submitted by K Sengupta
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Rating: 4.0000 (2 votes)
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Solution:
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m=3 gives 7m^4 – 3942 = -3375< 0. This is a contradiction.
m=5 gives 7m^4 – 3942 = 433, which is a prime number.
All primes m>5 must possess the form j Mod 10, when j= 1, 3, 7, 9, so that:
m^4 Mod 10= j^4 Mod 10 = 1.
Thus, (7*m^4 – 3942) Mod 5 = 0, whenever m is a prime number greater than 5.
Consequently, m = 5 is the only possible solution.
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Subject |
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Date |
 | solution | xdog | 2007-06-11 10:54:54 |
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