Recently I read the wonderful autobiography "I want to be a Mathematician" by Paul Halmos and came across the following passage:
"My first research was inspired by Carmichael. He told us about a peculiar question (inspired perhaps by the four square theorem): for which positive integers $a, b, c, d$ is it true that every positive integer is representable by the form $ax^2 + by^2 + cz^2 + dt^ 2$? (" Representable " - means via integral values of the variables $x, y, z, t$.) The answer is that there are exactly 54 such forms, and Ramanujan determined them all. My question was: which forms of the same kind represent every positive integer with exactly one exception? I found 88 candidates, proved that there could be no others, and proved that 86 of them actually worked. (Example: $x^2 + y^2 + 2z^2 + 29t^2$ fails to represent 14 only.)"
I googled but couldn't find anything about this cute problem. I would really like any reference for the work Ramanujan did on this problem and the aftermost work done by Halmos.
Thank you in advance!