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Monday, August 13, 2012

From Pedro A. Pisa in Scripta Mathematica, September 1954 — this identity:




1234 + 2484 + 3674 = 1254 + 2444 + 3694

… remains valid when the digits in each term are permuted in the same way:

1234 + 2484 + 3674 = 1254 + 2444 + 3694 
1243 + 2448 + 3647 = 1245 + 2444 + 3649 
1324 + 2844 + 3764 = 1524 + 2444 + 3964 
1342 + 2844 + 3746 = 1542 + 2444 + 3946 
1423 + 2448 + 3467 = 1425 + 2444 + 3469 
1432 + 2484 + 3476 = 1452 + 2444 + 3496 
2134 + 4284 + 6374 = 2154 + 4244 + 6394 
2143 + 4248 + 6347 = 2145 + 4244 + 6349 
2314 + 4824 + 6734 = 2514 + 4424 + 6934 
2341 + 4842 + 6743 = 2541 + 4442 + 6943 
2413 + 4428 + 6437 = 2415 + 4424 + 6439 
2431 + 4482 + 6473 = 2451 + 4442 + 6493 
3124 + 8244 + 7364 = 5124 + 4244 + 9364 
3142 + 8244 + 7346 = 5142 + 4244 + 9346 
3214 + 8424 + 7634 = 5214 + 4424 + 9634 
3241 + 8442 + 7643 = 5241 + 4442 + 9643 
3412 + 8424 + 7436 = 5412 + 4424 + 9436 
3421 + 8442 + 7463 = 5421 + 4442 + 9463 
4123 + 4248 + 4367 = 4125 + 4244 + 4369 
4132 + 4284 + 4376 = 4152 + 4244 + 4396 
4213 + 4428 + 4637 = 4215 + 4424 + 4639 
4231 + 4482 + 4673 = 4251 + 4442 + 4693 
4312 + 4824 + 4736 = 4512 + 4424 + 4936 
4321 + 4842 + 4763 = 4521 + 4442 + 4963

And everything above holds true if each term is squared.

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