Proofs

A medium difficulty HSC math problem on last-two-digits test for 4 with full step-by-step solutions.

A medium difficulty HSC math problem on leading digits of powers of two with full step-by-step solutions.

A medium difficulty HSC math problem on mersenne prime exponent cannot be even with full step-by-step solutions.

A hard difficulty HSC math problem on nested radicals and a cosine formula with full step-by-step solutions.

A easy difficulty HSC math problem on no positive integer difference of one with full step-by-step solutions.