find-all-numbers-with-any-number-of-digits-satisfying-abcd-xyz-2-zyx-dcba-

Question Number 198563 by mr W last updated on 22/Oct/23

f i n d a l l n u m b e r s (w i t h a n y n u m b e r

o f d i g i t s) s a t i s f y i n g

(\underset{―}{a b c d \dots x y z}) \times 2 = (\underset{―}{z y x \dots d c b a})

Answered by AST last updated on 25/Oct/23

2 z \equiv a (m o d 10); a ⩽ 4 \Rightarrow a \in {0, 2, 4}; a ⩾ z

a = 0 \Rightarrow z = 0; q u e s t i o n r e m a i n s t h e s a m e

a = 2 \Rightarrow z \overset{5}{\equiv} 1 \Rightarrow z = 6 \Rightarrow 2 b . . y 6 \times 2 = 6 b \dots y 2 X

a = 4 \Rightarrow z \equiv 2 (m o d 5) \Rightarrow z = 7 \Rightarrow (4 b \dots y 7) \times 2 = (7 y \dots b 4) X

N o s o l u t i o n . .

Commented by mr W last updated on 25/Oct/23

i a g r e e . t h a n k s!

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