## Le Monde puzzle [#1045]

**A**n minor arithmetic Le Monde mathematical puzzle:

Take a sequence of 16 integers with 4 digits each, separated by 2, such that it contains a perfect square and its sum is a perfect cube. What are the possible squares and cubes?

**T**he question is dead easy to code in R

for (x in as.integer(1e3:(1e4-16))){ if (max(round(sqrt(x+2*(0:15)))^2==x+2*(0:15))==1) { b=sqrt((x+2*(0:15))[round(sqrt(x+2*(0:15)))^2==x+2*(0:15)]) if ((round((2*x+30)^(1/3)))^3==(2*x+30)) print(c(x,b,(16*(x+15))^(1/3)))}}

and return the following solutions:

[1] 1357 37 28 [1] 5309 73 44

Nothing that exciting…!

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