about 5 years ago

Does 15x3 + 7x2 – 8x – 27 have an integer zero?

Proof and counterexample

about 12 years ago

Find all solutions in integers y and z to the equation 62 + y2 = z2.

Hey folks! I require some assistance here please with my course project. I need someone to answer this question promptly so that I may finish my project on time. To add something here, I am almost at a deadline so please be fast. Thank you very much guys! 

arold

about 12 years ago

Number Theory

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 because of my lack of knowledge in this subject. Please suggest a solution that I may narrate to him. Thank you!

alexey

about 12 years ago

Number Theory

Prove that there are an innite number of primes congruent to 3 mod 4.

We have formed a team in our college council where we provide resources to our subscribers related to exam material. I personally thought of including this question in it as well, because it is often tested in our exams. Please elaborate it.

alexey

about 12 years ago

Number Theory

"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 mind. Please suggest a solution so that I may compare it with the one that I have in my mind. Ty!

alexey

about 12 years ago

Number Theory

"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, : : : .)"

Hi! I am appearing for the entry test of a local top ranking university and need your help for preparations. Can you suggest a worthy answer to my question that meets high requirement standards? It will be highly appreciated. Thanks! 

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Recent questions in Number Theory

Does 15x3 + 7x2 – 8x – 27 have an integer zero?

Find all solutions in integers y and z to the equation 62 + y2 = z2.

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.)

Prove that there are an innite number of primes congruent to 3 mod 4.

"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."

"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, : : : .)"

"Find a positive integer n such that n=3 is a perfect cube, n=4 is a perfect fourth power, and n=5 is a perfect fth power."

Prove that there are no whole number solutions to the equation x2 - 15y2 = 31.

Find the number of solutions to the congruence x2 9 mod 23 112.

"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, : : : .)"

"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."

Prove that there are an innite number of primes congruent to 3 mod 4.