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September 20th, 2018, 12:47 PM   #21
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(1 - 2m)³ = (1 - 2m)(1 - 2m)²
=(1 - 2m)(2n+1)
=-4mn+2n-2m+1


for 4mn+2n-2m=-1

m=2n+1/4n+2
n=2m-1/-4m+2

replacing m and n by its value can we find the solution?

Last edited by Ak23; September 20th, 2018 at 12:49 PM.
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September 20th, 2018, 02:09 PM   #22
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I did all the calculation that gives
-4mn+2n-2m+1
(-4)*(1/2)*((-12)/3)+2*((-12)/3)-2*(1/2)+1=0

m=1/2
n=(-12)/3
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September 20th, 2018, 03:27 PM   #23
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(1 - 2m)³
(1-2*(1/2))^3=0

3n^2+3n+1
3*((-12)/3)^2+3*((-12)/3)+1=37
interprétation
-4mn+2n-2m+1
admits for solution 0 and 37 it is the minimum 0
for up to 37
0 1 7 19 37
7 and 19 are not cubes
the 1 yes which gives

64--27=37

3n^2+3n+1=1 = (1 - 2m)³=1
n=0
n=-1 m=0
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September 20th, 2018, 03:51 PM   #24
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I did the test of the theorem a ^ 3 + b ^ 3 = c ^ 3
based on
3n ^ 2 + 3n + 1 algorithm generating the difference between the consecutive cubes
the outgoing resultant is put under the cubic root if the whole spell is true.
If it interests you, I post algo. En following your method. I understood what it is.

Last edited by skipjack; September 20th, 2018 at 06:19 PM.
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September 20th, 2018, 06:25 PM   #25
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It''s known that a³ + b³ = c³ has no solution in positive integers, which implies that at least one of the cubes on the left-hand side is zero if the remaining cubes are integers.
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September 21st, 2018, 08:55 AM   #26
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a³+b³+c³=d³
3³+4³+5³=6³
but we can find the solution with 3 cubes.
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September 21st, 2018, 06:50 PM   #27
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if a+b=c
aⁿ+bⁿ=cⁿ it's false for any number.

c×aⁿ⁻¹+c×bⁿ⁻¹=cⁿ
2×5²+3×5²=5³
50 + 75 =125
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September 21st, 2018, 07:02 PM   #28
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Quote:
Originally Posted by Ak23 View Post
if a+b=c
aⁿ+bⁿ=cⁿ it's false for any number.
If a = 0 and b = c, it's true for any values of c and n.
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September 22nd, 2018, 03:58 AM   #29
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In proof of Wallis theorem,
you have:
A + B = C
ABC ≠ 0
A,B and C are relatively primes
B is divisible by 32
A = 3 mod 4 = 3
C = 1 mod 4 = 1
B = 32
n is prime ≤5
Aⁿ×Bⁿ×Cⁿ = (A×B×C)ⁿ
solving this with elliptic curves A + B ≠ C,
y²=x(x-3)(x+32)
y²=x³+29x²-96x

3+32=1

Last edited by skipjack; September 22nd, 2018 at 04:14 AM.
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September 22nd, 2018, 04:16 AM   #30
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What theorem of Wallis are you referring to? Is this related to your previous posts or are you digressing into a new topic?
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