In number theory, a branch of mathematics, Ramanujan's ternary quadratic form is the algebraic expression x2 + y2 + 10z2 with integral values for x, y and z.
[1][2] Srinivasa Ramanujan considered this expression in a footnote in a paper[3] published in 1916 and briefly discussed the representability of integers in this form.
After giving necessary and sufficient conditions that an integer cannot be represented in the form ax2 + by2 + cz2 for certain specific values of a, b and c, Ramanujan observed in a footnote: "(These) results may tempt us to suppose that there are similar simple results for the form ax2 + by2 + cz2 whatever are the values of a, b and c. It appears, however, that in most cases there are no such simple results.
W. Galway wrote a computer program to determine odd integers not expressible as x2 + y2 + 10z2.
[1] Based on Galway's computations, Ken Ono and K. Soundararajan formulated the following conjecture:[1] The conjecture of Ken Ono and Soundararajan has not been fully resolved.