It means that you cannot find two integers m and n such that m²+n² = 7. (1+4=5) < 7 < (4+4=8 ) Your book also says that 7 is the first integer that cannot be written like that a²+b²+c². 0 = 0²+0²+0² 1 = 1²+0²+0² 2 = 1²+1²+0² 3 = 1²+1²+1² 4 = 2²+0²+0² 5 = 2²+1²+0² 6 = 2²+1²+1² 7 = ? It is not possible to write 7, because next possible writing is 2²+2²+0² = 8 which is already too big. So 7 is the smallest one that cannot be written like this.

I might know what this is saying, but no guarantee. 0=0x0+0x0+0x0 1=0x0+0x0+1x1 2=0x0+1x1+1x1 3=1x1+1x1+1x1 4=0x0+0x0+2x2 5=0x0+1x1+2x2 6=1x1+1x1+2x2 7 is the first number that doesn't work for.