Palindromi & C.

[Bruno]

Dimostrare che esistono infiniti numeri non palindromi $\;q\;$ tali che $\;4\cdot q+3\;$ e $\;3\cdot q+2\;$ siano palindromi e non lo sia $\;2\cdot q+1$.

[Quelo]

$\displaystyle q=2+285\sum_{k=0}^n 10^{3k+1}=2+2850/+2850000/+2850000000/+...$ non palindromo

$\displaystyle 4q+3=11+1140\sum_{k=0}^n 10^{3k+1}=11+11400/+11400000/+11400000000/+...$ palindromo

$\displaystyle 3q+2=8+855\sum_{k=0}^n 10^{3k+1}=8+8550/+8550000/+8550000000/+...$ palindromo

$\displaystyle 2q+1=5+570\sum_{k=0}^n 10^{3k+1}=5+5700/+5700000/+5700000000/+...$ non palindromo

[Bruno]

Ottimo, Sergio

Due esempi:

2 852 852 852
3 + 4×2852852852 = 11411 4 11411
2 + 3×2852852852 = 8558 55 8558
1 + 2×2852852852 = 570 570 570 5

2 852 852 852 852 852
3 + 4×2852852852852852 = 11411411 4 11411411
2 + 3×2852852852852852 = 8558558 55 8558558
1 + 2×2852852852852852 = 570 570 570 570 570 5