Recent questions in Number Theory

Number Theory

arold
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 proje...
arold
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...
alexey
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...
alexey
"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...
alexey
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 wi...
nicoline
"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 quest...
alexey
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 solu...
alexey
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 wi...
alexey
"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...
alexey
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...