I am trying to minimize y=a+b+c+...+x (all integers) for the function 25^25=a24^25+b23^25+c22^25+...+x1^25
I have tried multiple forms of the FindMinimum() but Mathematica keeps giving me errors I don't understand I use FindMinimum because I also want to know each individual value for a to x where y is minimal.
This is currently my best code:
FindMinimum[{a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s + t + u + v + w + x,
25^25 = a*24^25 - b*23^25 - c*22^25 - d*21^25 - e*20^25 - f*19^25 -
g*18^25 - h*17^25 - i*16^25 - j*15^25 - k*14^25 - l*13^25 -
m*12^25 - n*11^25 - o*10^25 - p*9^25 - q*8^25 - r*7^25 - s*6^25 -
t*5^25 - u*4^25 - v*3^25 - w*2^25 - x*1^25 &&
a \[Element] Integers && b \[Element] Integers &&
c \[Element] Integers && d \[Element] Integers &&
e \[Element] Integers && f \[Element] Integers &&
g \[Element] Integers && h \[Element] Integers &&
i \[Element] Integers && j \[Element] Integers &&
k \[Element] Integers && l \[Element] Integers &&
m \[Element] Integers && n \[Element] Integers &&
o \[Element] Integers && p \[Element] Integers &&
q \[Element] Integers && r \[Element] Integers &&
s \[Element] Integers && t \[Element] Integers &&
u \[Element] Integers && v \[Element] Integers &&
w \[Element] Integers && x \[Element] Integers },
{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x}]