Find a sequence of consecutive integers, a, a+1, a+2, ..., b such that b is a square and that: [a+(a+1)+(a+2)+...+(b-1)]b and [(a-1)+a+(a+1)+(a+2)+...+(b-1)]b are both 10-digit numbers containing all of the digits 0 to 9.
a=78, b=1296 which is 36^2
[a+(a+1)+(a+2)+...+(b-1)]b = (78+79+80+.........+1295)*1296 =1083659472 and:
[(a-1)+a+(a+1)+(a+2)+...+(b-1)]b = (77+78+79+80+.....+1295)*1296 = 1083759264
It is observed that each of these two expressions is a 10-digit number containing each of the digits fron 0 to 9.
For an explanation, refer to the solution submitted by Charlie in this location.
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