Use Python to solve the problem please!

Euler's Conjecture On Sums of Like Powers In 1769 Leonhard Euler considered the following to be true: For all integers n,k>1, if the sum of nkth powers of positive integers is itself a k-th power than nk a1k+a2k++ank=bknk COUNTEREXAMPLE TO EULER'S CONJECTURE ON SUMS OF LIKE POWERS BY L. J. LANDER AND T. R. PARKIN Communicated by J. D. Swift, June 27,1966 A direct search on the CDC 6600 yielded 276+845+1105+1336=1445 as the smallest instance in which four fifth powers sum to a fifth power. This is a counterexample to a conjecture by Euler [1] that at least nnth powers are required to sum to an nth power, n>2. Problem 1 1. Write a Python (no Numpy) program to compute the solution. Consider the following intervals for your computation: 2080100120140a140a2100a3120a4140b160 2. Compute the execution time (using timeit https://docs.python.org/3/library/timeit.html