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Find all solutions in integers y and z to the equation 62 + y2 = z2.
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Let a and b be positive integers. Show that (ab)(gcd(a; b)) = (a)(b) gcd(a; b). (Example: If a = 12 and b = 8, the equation reads 32 2 = 4 4 4.)
My little bro is going to have his intermediate exams soon and he needs some assistance. At first he asked me this question, but I turned him down bec...
Prove that there are an innite number of primes congruent to 3 mod 4.
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"Fermat showed that 237 -1 is composite by nding a prime factor p of 237 -1 which lies between 200 and 300. Using your knowledge of number theory, deduce the value of p."
Hey! I wanted to ask whether my question has any reasonable answers. I am doing my home assignment and I’m not quite sure about the answer I have in m...
"Which positive integers m have the property that there is a primitive root mod m? (Summarize what we know about this question, and why we know it. Your answer should be clear enough that one could use it to decide immediately if there is a primitive root modulo (257)2, 4 661, 257 661, : : : .)"
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Find the number of solutions to the congruence x2 9 mod 23 112.
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