What is the sum of the smallest and second-smallest positive integers \(a\) satisfying the congruence
\(27a\equiv 17 \pmod{40}~?\)
27a = 17 (mod 40) 27 mod 40 = 27 + 13 27*2 mod 40 = 14 27*5 mod 40 = 15 27*8 mod 40 = 16 27*11 mod 40= 17 a = 40m + 11, where m =0, 1, 2, 3......etc. The smallest value of "a" =[40*0 + 11] = 11 The 2nd smallest value of "a" =[40*1 + 11] = 51
The sum =11 + 51 = 62
+586 
