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In the equation, (X4)^n - (Y7)^n = p, n is a positive intege
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12 Nov 2017, 00:40
12 Nov 2017, 00:40
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In the equation, \((X4)^n - (Y7)^n = p\), n is a positive integer, and X and Y can be any integer between 1 and 9, meaning that X4 and Y7 are both two-digit integers. What are all the possible values of the units digit of p if p > 0?
[A] 1
[B] 2
[C] 3
[D] 4
[E] 5
[F] 6
[G] 7
[H] 8
[I] 9
Kudos for correct solution.
[A] 1
[B] 2
[C] 3
[D] 4
[E] 5
[F] 6
[G] 7
[H] 8
[I] 9
Kudos for correct solution.
Show: :: OA
[A], [E], and [G].
Re: In the equation, (X4)^n - (Y7)^n = p, n is a positive intege
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13 Nov 2017, 00:29
13 Nov 2017, 00:29
3
Since we are asked for the unit digit of a number, we can forget about the tens digit and just focus on the two unit digits, 4 and 7.
We know there are patterns governing the unit digits of numbers, such that multiples of 4 have digits as 4, 6, 4, 6, 4, ..., while multiples of 7 go as 7, 9, 3, 1, 7, ...
Here we see the numbers ending in 4 and 7 has the same exponent, thus the results will have units digit as 4+7 = 11, 6+9 = 15, 4+3 = 7, 6+1 = 7, 4+7 = 11, ...
Among our answer we have to choose A, E and G
We know there are patterns governing the unit digits of numbers, such that multiples of 4 have digits as 4, 6, 4, 6, 4, ..., while multiples of 7 go as 7, 9, 3, 1, 7, ...
Here we see the numbers ending in 4 and 7 has the same exponent, thus the results will have units digit as 4+7 = 11, 6+9 = 15, 4+3 = 7, 6+1 = 7, 4+7 = 11, ...
Among our answer we have to choose A, E and G
Re: In the equation, (X4)^n - (Y7)^n = p, n is a positive intege
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08 Aug 2021, 02:16
08 Aug 2021, 02:16
why not option c.
