(3²⁵ + 3²⁶ + 3²⁷ + 3²⁸) = 3²⁵ x (1 + 3 + 3² + 3³) = 3²⁵ x 40

     = 3²⁴ x 3 x 4 x 10

     = (3²⁴ x 4 x 30), which is divisible by30.

Let x = 6q + 3.

Then, x² = (6q + 3)²

   = 36q² + 36q + 9

   = 6(6q² + 6q + 1) + 3

Thus, when x² is divided by 6, then remainder = 3.

Let the numbers be a and b. Then, a + b = 12 and ab = 35.

	a + b	=	12			1	+	1		=	12
	ab		35			b		a			35

Sum of reciprocals of given numbers =	12
	35

When n is even. (xⁿ - aⁿ) is completely divisibly by (x + a)

(17²⁰⁰ - 1²⁰⁰) is completely divisible by (17 + 1), i.e., 18.

    (17²⁰⁰ - 1) is completely divisible by 18.

    On dividing 17²⁰⁰ by 18, we get 1 as remainder.

1400 x x = 1050   ==>   x =1050=314004