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Compute $2^{32} \; \mod \; 37$

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$2^2\equiv 4\; \mod \; 37\\
2^4 \equiv 16 \; \mod \; 37\\
2^8 \equiv 256 \equiv 34 \; \mod \; 37\\
2^{16} \equiv (-3)^2 \equiv 9 \; \mod \; 37\\
2^{32} \equiv 81 \; \mod \; 37\\
2^{32} \equiv 7 \; \mod \; 37$
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To calculate 2³² mod 37

=(2⁸)⁴ mod 37 = (256)⁴ mod 37 

=(256 mod 37)⁴ mod 37

=(-3)⁴ mod 37 = 81 mod 37 = 7

7 is the answer.

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