Question

Jika bilangan bulat x dan y dibagi 4, maka bersisa 3. Jika bilangan x – 3y dibagi 4 maka akan bersisa berapa?

Answer 1

X/4 = k, sisa = 3 ----> x = 4k + 3
y/4 = m, sisa = 3 ----> y = 4m + 3 -----> 3y = 12m + 9

perhatikan bahwa :
x - 3y = 4k+3-(12m+9) = 4k - 12m - 6 = 4(k - 3m - 1) - 2
maka jika x - 3y dibagi 4, sisanya adalah :
(4(k - 3m - 1) - 2) / 4 = k - 3m - 1, sisanya = 2


cara lain :
gunakan trials, misal x = 31 dan y = 7
x/4 = 31/4 = 7, sisa = 3
y/4 = 7/4 = 1, sisa = 3
maka
(x - 3y)/4 = (31 - 3(7)) / 4 = (31 - 21) / 4 = 10/4 = 2, sisa = 2