| 1 | 1 | |||
wykaż że jeżeli liczba x + | jest liczbą całkowitą to liczba x3 + | jest też | ||
| x | x3 |
| 1 | x6+1 | |||
x3 + | = | |||
| x3 | x3 |
| 1 | 1 | 1 | 1 | 1 | ||||||
x3+ | =(x+ | )(x2−1+ | )=(x+ | )((x+ | )2−3) | |||||
| x3 | x | x2 | x | x |
| 1 | 1 | 3 | 1 | 1 | ||||||
x3+ | =(x+ | )3−3x− | =(x+ | )3−3(x+ | ) | |||||
| x3 | x | x | x | x |
| 1 | 1 | |||
=(x+ | )(( x+ | )2 −3) | ||
| x | x |