Each of x and y is a positive integer that satisfies this equation:
x
oC=y
oF
Determine the minimum value of x+y such that:
x is a triangular number and, y is a
heptagonal pyramidal number.
What is the next smallest value of x+y?
***
oF = (9/5)*
oC+32, where
oF represents degree Fahrenheit and,
oC represents degree Celsius.
There is a classic problem called the "Cannonball Problem". We have a version of that problem with "
S.o.S is S". The relevance to this problem is that both problems can be reduced to finding integer points (x,y) on a curve of the form y^2 = ax^3 + bx^2 + cx + d, which is a form of an
elliptic curve!
In "S.o.S is S", I noted that it has been proven that there exactly two solutions to that problem, and I suspect we have the same sort of thing here. That is to say the two solutions, (x,y) equals (630, 1166) or (820, 1508), found by Charlie and Larry are in fact ALL the positive integer solutions.
Not a Cannonball
