Verification Calculations for Trivia Propositions
This is a verification calculation within a limited scope for Trivia Proposition No. 30, inspired by Fermat’s Last Theorem.
| \(\normalsize \hspace{10px} {\large \displaystyle \sum_{\small j=0}^{\small n-1}}(a+j)^n=b^n,\hspace{20px} n\ge 4 \\\) |
There are no natural numbers a and b satisfying this equation for a natural number n≧4.
If b exists within the specified search range, the values of a and b are shown for each n.
If no b exists in that range, -- is shown for each n.
Note 1) Set the calculation precision to approximately n+1 times the maximum number of digits in a.
Note 2) An excessively large search range will time out.
Solutions to the equation above exist for n=2 and n=3.
n=2, 32+42=52, 202+212=292, ...
n=3, 33+43+53=63
---Fermat’s Last Theorem ----------------
For an integer n greater than or equal to 3, Xn+Yn=Zn
there are no natural numbers X,Y,Z satisfying this equation
Note 2) An excessively large search range will time out.
Solutions to the equation above exist for n=2 and n=3.
n=2, 32+42=52, 202+212=292, ...
n=3, 33+43+53=63
---Fermat’s Last Theorem ----------------
For an integer n greater than or equal to 3, Xn+Yn=Zn
there are no natural numbers X,Y,Z satisfying this equation
No customer feedback for this calculation yet.