Explicație pas cu pas:
Scriem abcd(barat) in baza 10:
abcd(barat)=1000a+100b+10c+d
Scriem dcba(barat) in baza 10:
dcba(barat)=1000d+100c+10b+a
Adunam cele doua numere:
abcd(barat)+dcba(barat)=1000a+100b+10c+d+1000d+100c+10b+a=1001a+110b+110c+1001d=1001*(a+d)+110*(b+c)
Stim ca daca avem doua numere x si y, (x+y)²=x²+y²+2xy. Aplicam aceasta formula:
[abcd(barat)+dcba(barat)]²=[1001*(a+d)+110*(b+c)]²=[1001*(a+d)]²+[110*(b+c)]²+2*1001*110(a+d)(b+c)=1001²(a+d)²+110²(b+c)²+22020(a+d)(b+c)=1002001(a+d)²+12100(b+c)²+22020(a+d)(b+c)=Dam factor pe 121=121*[8281(a+d)²+100(b+c)²+1820(a+d)(b+c)]
Am reusit sa scriem suma [abcd(barat)+dcba(barat)]², ca un multiplu de 121.
Deci, numarul [abcd(barat)+dcba(barat)]² este divizibil cu 121.
