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image of colourful numbers.Can you convince me of each of the following?

  • The pattern below continues forever: $$8^2 = 7^2 + 7 + 8$$ $$9^2 = 8^2 + 8 + 9$$
  • If a square number is multiplied by a square number the product is ALWAYS a square number.
  • No number terminating in $2, 3, 7$ or $8$ is a perfect square.