Recent questions in Number Theory

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arold-avatar
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! 
6
arold-avatar
about 12 years ago

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!
6
alexey-avatar
about 12 years ago

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.
7
alexey-avatar
about 12 years ago

"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!
6
alexey-avatar
about 12 years ago

"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! 
6
1-6 of 9
nicoline-avatar
about 12 years ago

"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."

I have various answers to this question but I’m not sure if they are worth presenting, so kindly tell me a complete and appropriate answer to my question.
6
alexey-avatar
about 12 years ago

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

How am I supposed to answer this question when it’s not even in my syllabus?  I had given my board exams recently. Please suggest an appropriate solution so that my preparation becomes more efficient next time. Thanks!
6
alexey-avatar
about 12 years ago

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

Hello! I am a student of Masters. I have to submit my thesis on this topic so I need your help in preparing it. Kindly help me in this situation. I will be very thankful for your concerns.
6
alexey-avatar
about 12 years ago

"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! 
6
alexey-avatar
about 12 years ago

"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!
6
alexey-avatar
about 12 years ago

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.
7
1-6 of 9
Number Theory