Euler's sum of powers conjecture, if a sum of $k$th powers is a $k$th power, then the sum has at least $k$ terms.

Proposed by Euler in 1769. Counterexample for $k=5$ found in 1966, for $k=4$ in 1986.

Euler's sum of powers conjecture, if a sum of $k$th powers is a $k$th power, then the sum has at least $k$ terms.

Proposed by Euler in 1769. Counterexample for $k=5$ found in 1966, for $k=4$ in 1986.

Euler's sum of powers conjecture, if a sum of $k$th powers is a $k$th power, then the sum has at least $k$ terms.

Proposed by Euler in 1769. Counterexample for $k=5$ found in 1966, for $k=4$ in 1986.

Euler's sum of powers conjecture, if a sum of $k$th powers is a $k$th power, then the sum has at least $k$ terms.

Proposed by Euler in 1769. Counterexample for $k=5$ found in 1966, for $k=4$ in 1986.