User:Bhowmickr
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an − bn = c2 − d2 like 73 − 43 = 482 − 452 xn = z2 − y2 like 33 = 142 − 132 , an − bn = (a − b)n + nk(a − b),here when "a" is odd natural number and "b" is any natural number and "n" is any prime or its factors are the same prime(here the multiples of 5 like 25,125 etc. are excluded but the case of 5 is included) then "k" will always be a natural number. From this it can be proved very easily and in an elementary way that it is impossible to write
an − bn = xn
or
an = xn + bn
for n>2.
