# Odd Numbers Not Expressible as Sum of 5 Distinct Non-Zero Coprime Squares

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## Theorem

The largest odd positive integer that cannot be expressed as the sum of exactly $5$ non-zero square numbers all of which are coprime is $245$.

## Proof

## Sources

- 1994: Paul T. Bateman, Adolf J. Hildebrand and George B. Purdy:
*Sums of Distinct Squares*(*Acta Arith.***Vol. 67**,*no. 4*: pp. 349 – 380)

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $157$