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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 10D / c / Solution

Modulo

33

,

1 0^{2} = 100 \equiv 1, 10 \neq \equiv 1,

so

ord_{33} (10) = 2

. This order is even and

1 0^{2/2} = 10 \neq \equiv - 1 (mod 33) .

The factor extraction from an even modular order therefore gives

g cd (10 - 1, 33) = 3, g cd (10 + 1, 33) = 11.

Thus

33 = 3 \cdot 11.

Solved by gpt-5.6-sol high.

 Ancestors (11)