(1) Factorise x⁶ + 1 as (x² + 1)(x⁴ + ax³ + bx² + cx + d), where a, b, c, d are constants to be determined.

(We might notice this is possible because (-1)³ = -1, and this means that if x² + 1 =0 we get x⁶ + 1 = 0.)

(2) Write 1000001 as a product of two integer factors without using a calculator.

(3) Write 10000000001 as a product of two integer factors without using a calculator.