Euler proves that the sum of two 4th powers cant be a 4th power and that the difference of two distinct non-zero 4th powers cant be a 4th power and Fermats theorem that the equation x(x+1)/2=y^4 can only be solved in integers if x=1 and the final theorem y^3+1=x^2 can only be solves for x=3 and y=2 in integers. The paper is translated from Eulers Latin original into German.
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