Find an Unrelated Number
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1


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Takes inputs separated by space (or any single non-newline character)

Replaces all digits with 1, and joins the resulting numbers with another 1.

Proof of correctness

Courtesy of Martin Ender


This operation computes a result with one more digit than the number of digits of the two numbers together; the only operation that could produce a result so big is exponentiation.
The result is a repunit (a number whose digits are all 1).
"It is know [sic] [...] that a repunit in base 10 cannot [...] be a perfect power." This means that this result can't be produced by exponentiation either.