若一個(gè)兩位正整數(shù)m的個(gè)位數(shù)為4,則稱(chēng)m為“好數(shù)”.
(1)求證:對(duì)任意“好數(shù)”m,m
2-16一定為20的倍數(shù);
(2)若m=p
2-q
2,且p,q為正整數(shù),則稱(chēng)數(shù)對(duì)(p,q)為“友好數(shù)對(duì)”,規(guī)定:
,例如24=5
2-1
2,稱(chēng)數(shù)對(duì)(5,1)為“友好數(shù)對(duì)”,則
,求小于70的“好數(shù)”中,所有“友好數(shù)對(duì)”的H(m)的最大值.