General Diophantine Equations
1729 can be expressed as the sum of two perfect cubes in two distinct ways.
How many such numbers exist?
Hint: Given one set of such numbers, how could you construct another set?
by
Adhiraj Mandal
If \(a\) and \(b\) are integers such that \(a^3+b^3=2015\), then what is \(a+b\)?
by
Andy Hayes
\[\LARGE{2 + 2 = 2 \times 2 \\ 1 + 2 + 3 = 1 \times 2 \times 3}\]
In the above equations, there are respectively 2 and 3 positive integers whose sum is equal to their product.
Find 4 positive integers whose sum is equal to their product. Enter the answer as their sum
by
Nihar Mahajan
Find the positive integer \(n \) such that \(n^3 + 2n^2 + 9n + 8 \) is a perfect cube.
by
Nelson Mandela
\[ a + b + c + d + e = a \times b \times c \times d \times e \]
How many unordered 5-tuples of positive integers are there which satisfy the above equation?
by
Calvin Lin