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What is the units digit for the number 123^(456) ?

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a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

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A Biggy

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

Negative Power

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
  • What does $4$ to the power $3$ mean ?
  • What does $4$ to the power $-3$ mean ?
  • What does $-4$ to the power $3$ mean ?
  • What does $-4$ to the power $-3$ mean ?