a) Replace each letter in the following sum by a digit from 0 to 9, in such a way that the sum is correct.\tab \tab ABC
\tab \tab DEF
+GHI
\tab \tab \tab JJJDifferent letters must be replaced by different digits, and equal letters must be replaced by equal digits. Numbers ABC, DEF, GHI and JJJ cannot begin by 0.b) Determine how many triples of numbers (ABC,DEF,GHI) can be formed under the conditions given in a). modular arithmeticnumber theory unsolvednumber theory