> 3^2 + 4^2 = 5^2> 3^3 + 4^3 + 5^3 = 6^3>3 ^4 + 4^4 + 5^4 + 6^4 = 7^4 + 143this shit is retarded and I hope it gets patched
Why should it get patched?>odd * odd = odd>even * even = evenso >odd ^ n = odd>even ^ n = evenHence >>odd + even + odd + even = odd + odd + even + even = even + even + even = evenObviously those things can never be equal.
>>16881555Not OP but obviously the issue is +143.
>>16881545>7^4 + 143143 = 12^2 – 1
>>16884068And there it is.Bravo.
>>16881545Sequence of squares;1,4,9,16,25n^2The difference of each consecutive increase of n' is 2n-1∑(2n−1)=n2Sequence of summing consecutive squares:1,,5, 14, 30, 55, 91k=1∑nk2=6n(n+1)(2n+1)
Picrel for sum of consecutive squares, now, onto the Sequence of cubes:1,8,27,64,125 = n^3Differences between sequence of cubes:7,19,37,61General form:n^3−(n−1)^3=3n^2−3n+1Second differencesCompute differences of 3n^2−3n+1:12, 18, 24Δ2(n3)=6nThird differences6,6Δ3(n3)=6Constant third difference cubic polynomial (discrete analogue of calculus)
>>16884362Summing consecutive cubesCumulative sums:1, 9, 36, 100, 225
Now, onto the Sequence of fourth powers, sum of fourth powers, and differences of fourth powers.Sequence of n^41, 16, 81, 256, 625First differences of fourth powers15, 65, 175, 369So:Δ(n^4)=4n^3 − 6n^2 + 4n−1Second differences50, 110,194Δ^2( n^4)=12n^2 − 12n+2Third differences:60, 84Δ3(n4)=24n−12Fourth differences:24Fourth differences (constant)Δ4(n4)=24Δ^4 (n^4)=24=4!
