Yes, n=[(n+1)/2]^2-[(n-1)/2]^2 A special case of: ab=[(a+b)/2]^2-[(a-b)/2]^2 Like 19x1=100-81=19 18x2=100-64=36 17x3=100-49=51 16x4=100-36=64 15x5=100-25=75 14x6=100-16=84 13x7=100-9=91 12x8=100-4=96 11x9=100-1=99 10x10=100-0=100
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331 is a difference between two cubes in any base—octal, decimal, etc
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1+2+3+...+n=n×(n+1)/2 Proof: 1) Draw 1,2,...,n ░░ ░░ ░░ ░░ ░░ ░░ 2) Duplicate and rotate it by 180° ▓▓ ▓▓ ▓▓ ▓▓ ▓▓ ▓▓ 3) Put them together to form a rectangle of size n×(n+1) ░░ ▓▓ ▓▓ ▓▓ ░░ ░░ ▓▓ ▓▓ ░░ ░░ ░░ ▓▓
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two CONSECUTIVE squares
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Not necessarily, I mean, "6^2 - 3^2 = 36 - 9 = 27"
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Or you could use : (k+1)^2-k^2 = 2k+1 for every integer
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Alternatively, since every odd can be written as 2k+1=1(2k+1)=(k+1-k)(k+1+k)=(k+1)²-k²

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(k+2)^2 =k^2 +4(k+1) shows that multiples of 4 are also differences of 2 squares. These and the odd integers are the only integers that are the difference of 2 squares.
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Wow so for any 2 consecutive numbers, add them together and that is the difference of their squares?
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I went to public schools but our town had an amazing “gifted & talented program” for the 2 kids with the highest iqs from each elementary school. in that program all we did was learn in this exact manner. I never realized how much it shaped my learning until your tweets! Ty

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The sad thing is that if those who weren’t as gifted learned it this way they would probably “get it”...:-)
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