[理工] [離散]等價類

[jim055006 (好崩潰)]

On the set Z of all integers, define the relation R by
R={(a,b)屬於ZxZ|a^2-b^2 is divisible by 5}. Show that
R is equivalence relation. Find the equivalence classes
of this equivalence relation on Z.

證明等價關係我會
至於要找等價類我想應該是[0][1][2][3][4]
可是答案是說[0][1][2]
不太懂為什麼..
有請高手幫忙解惑
鋼溫!!           

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 223.138.240.24
→ Byzantin:[1] = [4] , [2] = [3]
→ jim055006:不太懂...有勞B大可以說仔細一點嗎?
→ vanillaXleft:4^2-1^2=16-1=15 ,so [1]=[4]
推 RebeccaHall:其實1樓說得很清楚了.. 寫 [0] [1] [2] 等同
→ RebeccaHall:[0] [1]=[4] [2]=[5]
→ jim055006:感謝V大...我想應該是懂了