Modular primes.
Number Theory
Level
2
If p is any prime greater than 5 and , what are the positive integers values of x that satisfy the equation?
1, 3 and 4
1
1 and 5
2 and 5
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1 solution
P can be written as one of the following expressions: 6y, 6y+1, 6y+2, 6y+3, 6y+4, and 6y+5, as these allow for all possible values of x mod6. 6y cannot be prime because 6 can be factored out of it. 6y+2 and 6y+4 cannot be prime because 2 can be factored out of them. 6y+3 cannot be prime because 3 can be factored out of it. Therefore p can only be written as 6y + 1 or 6y + 5, so x must be either 1 or 5.