100 ^ 2013 =
= 100 × 100^2012 =
= (36 + 64) × 100^2012 =
= 36 × 100^2012 + 64 × 100^2012 =
= 6^2 × (100^1006)^2 + 8^2 × (100^1006)^2 =
= (6 × 100^1006)^2 + (8 × 100^1006)^2
Am scris numărul 100^2013 ca o sumă de doua pătrate perfecte.
100²⁰¹³ =
= 100²⁰¹²ₓ100
= 100²⁰¹²ₓ(64+36)
= (100¹⁰⁰⁶)²(8²+6²)
= 8ₓ100¹⁰⁰⁶)² + (6ₓ100¹⁰⁰⁶)²
