Book Maths Puzzle Category

1^12 + 2^13 +3^12+ 4^13 +5^12 upto 60^13 is divisible by 60,61,63,65
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Book Other Question

If

(x^2) + (y^2) = z^3 ;

(x^3) + (y^3) = p^2 ;

where x, y, z, p are whole no. ( W )

Find any possible value of x , y , z ,p that satisfy the above two equations.


An equilateral triangle of side 1 unit is taken . it is circumscribed by a circle. the circle in turn is circumscribed by another equilateral triangle. This process is repeated till there are 5 equilateral triangles. what is the side of the largest equilateral triangle?