Suppose x, pЄ Z such that p is prime. If 5401 (mod p) 740 = 1 (mod p) find the least positive integer e such that it must be true (for any possible value of x satisfying the congruences above) that 1 (mod p).

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Supposex, p € Z such that p is prime. If
x5401 (mod p)
x7401 (mod p)
find the least positive integer e such that it must be true (for any possible value of a satisfying the congruences above) that
x = 1
(mod p).
(Hint: consider taking products of 540, 740 or try small examples like x = 2, p = 7.)
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Transcribed Image Text:Supposex, p € Z such that p is prime. If x5401 (mod p) x7401 (mod p) find the least positive integer e such that it must be true (for any possible value of a satisfying the congruences above) that x = 1 (mod p). (Hint: consider taking products of 540, 740 or try small examples like x = 2, p = 7.) Type your answer...
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