Dear Researchers,
Kindly let me know about 5 top most research problems in number theory which are concerning to
Double series and / or combinatorics
Issam Kaddoura
Dear M. P. Chaudhary
The following problems are active and exciting.
(1) Beal's conjecture.
(2) Collatz problem.
(3) The Goldbach conjecture.
(4) Gaps between prime numbers.
(5) Twin primes conjecture.
(6) Riemann Hypothesis.
Best regards
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Louis John Scheinman
How about the solution of the cubic Pythagorean Diophantine equation x^3+y^3+z^3=a^3. This is the equation that interests me if anyone has any new insight into it.
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Juan Weisz
Know this identity?
x^3 + y^3 +z^3 -3xyz =(x+y+z) (x^2 +y^2 +z^2 -xy-xz-yz)
Obviously you cannot have a=0
Sum of 2 cubes is special case of this.
How about x=a, y=-z?
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