A 6-digit number is a square as well as a cube,If 6 is substracted from this we get a prime number.Find the number
2006-12-11 01:59:06 · 7 answers · asked by VIPIN J 1 in Science & Mathematics ➔ Mathematics
Well, if it's both a square and a cube, it must also be some number raised to the 6th power.
Just playing with the calculator, it appears only 7, 8, and 9 are candidates:
7^6 = 117649 - 6 = 117643
8^6 = 262144 - 6 = 262138 (even so not prime)
9^6 = 531441 - 6 = 531435 (sum of digits divisible by 3 so divis by 3)
So it must be 117643.
2006-12-11 02:14:20 · answer #1 · answered by Jim Burnell 6 · 0⤊ 0⤋
The number is 117649.
The condition that a number "x" cubed would be equal to another number "y" being square imposes that "x" be square itself. There are only 3 two digits squares that will yield a 6 digit numbers when cubed: 46, 64 and 81.
But 64 cubed is an even number, and subtracting 6 from it will still make that number even so it cannot be prime. 81 cubed is 531441, but if you subs tract 6, the number ends with 5, and is thus divisible by 5, and thus not a prime.
This leaves 49 cubed (117649) as the only candidate, and true enough 117643 is prime (I did not want to spend too much time testing all the primes from 3 to 341 for fit, so I went to the site http://www.amblesideprimary.com/ambleweb/primenumber/primecheck.htm to check if the number was prime, and it is)
2006-12-11 10:23:29 · answer #2 · answered by Vincent G 7 · 0⤊ 0⤋
100000=
x=8 ==> x^6-6 modulo 2=0
==> x=7
==> x^6=117649
2006-12-11 10:34:41 · answer #3 · answered by mydecember_8t8 1 · 1⤊ 0⤋
Try 117649.
I was about to prepare a detailed trial & error method, but it didn't require too many trials...
117649 = 343^2.
117649 = 49^3.
117649 - 6 = 117643, you can got to www.prime-numbers.org to check whether it's prime!
2006-12-11 10:14:01 · answer #4 · answered by Bugmän 4 · 0⤊ 0⤋
Try 117649.
117649 = 343^2.
117649 = 49^3.
117649 - 6 = 117643, you can got to www.prime-numbers.org to check whether it's prime!
2006-12-12 00:07:03 · answer #5 · answered by arpita 5 · 0⤊ 0⤋
abcdef - 6 = z
and
abcdef = x^2
abcdef = y^3
then: abcdef = t^6
t must be or 7, 8 or 9
testing: t = 7
117649
2006-12-11 10:11:50 · answer #6 · answered by Culebrin 2 · 2⤊ 0⤋
Why don't you try and find a solution? That way, you can learn better!
2006-12-11 10:47:18 · answer #7 · answered by Sami V 7 · 0⤊ 0⤋