9 som faktor

[mny]

Hei!

Jeg tenker på et tosifret tall, la oss si 82, trekker så i fra det baklengse tallet (28) og får 54. Alle tosifrede tall jeg gjør slik med får 9 som felles divisor, og tverrsummen blir alltid 9.

Så skal jeg vise at svaret alltid vil ha 9 som faktor.

Jeg prøver slik:

T = 10a + b

trekker fra det baklengse tallet Q = 10b + a på denne måten:

T - Q = (10a + b) - (10b + a) = 10a + b - 10b - a = 9a - 9b = 9 (a - b)

Har jeg nå vist at svaret alltid vil ha 9 som faktor, eller er jeg ikke helt i mål?

Hilsen Morten

-it's never too late

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Så greit ut det

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