There are two four digit numbers that satisfy condition 1. 1458: sum digits is 18 and 18 ∙ 81 = 1458 1729: sum digits is 19 and 19 ∙ 91 = 1729.

But 1458 does not satisfy condition 2, so we delete it. 1729 does satisfy condition 2: 9271 = 73 ∙ 127 and (73^2 + 127^2) / 2 = 10729.

## mysterie number

There are two four digit numbers that satisfy condition 1.

1458: sum digits is 18 and 18 ∙ 81 = 1458

1729: sum digits is 19 and 19 ∙ 91 = 1729.

But 1458 does not satisfy condition 2, so we delete it.

1729 does satisfy condition 2: 9271 = 73 ∙ 127 and

(73^2 + 127^2) / 2 = 10729.