TV MATH

1. What type of curve is generated by the equation y² = 4ax was asked during a math competition. Name the curve.
2. 28 was claimed to be a perfect number. Verify the claim.

Answers

1. A prabola which opens to the right is the curve generated by the equation y² = 4ax where a is the distance from the point of origin. The curve is symetric about the x-axis.
2. A perfect number is a number whose factors, exculding the numbers itself, add up to the given number. The factors of 28 are 1, 2, 4, 7, and 14. 1 + 2 + 4 + 7 + 14 = 28. The sum of the factors excluding the given numbers equals the given number. 28 is a perfect number.

   Perfect numbers are given by the formula 2^{n - 1}(2ⁿ - 1). Picking any number for n generates a specific perfect number. Let n = 3. 2^{3 - 1}(2³ - 1 = 2²(2³ - 1 = 2²(8 - 1) = 2²(7)= 4 * 7 = 28. 28 is the third perfect number.