一般解有（1，2），（2，1），（9，15）……求质数解，没有好的方法？令没p=/m，q=/m解一次不定方程，m取1，2，…试求

{17,5}
{107,7}
{233,17}
{727,17}
{1423,43}
{1487,107}
{2609,53}
{3767,37}
{5527,347}
{6619,173}
{7577,89}
{9619,31}
{12329,113}
{13907,317}

解很多的，仅考虑p>q的素数解。
在q小于1000时有116组解，q小于10000时有935组解。
q<1000的解如下：（）内部为倍数 (p^2+3q)/(q^2+3p)
q=5: p=17(4)
q=7: p=107(31)
q=17: p=233(55),727(214)
q=31: p=9619(3103)
q=37: p=3767(1120)
q=43: p=1423(331)
q=53: p=2609(640)
q=89: p=7577(1873),114859(37426)
q=107: p=1487(139)
q=109: p=57709(18001)
q=113: p=12329(3055),236231(77350)
q=127: p=47147(14107)
q=137: p=18233(4525)
q=149: p=21617(5368),543929(178876)
q=163: p=197371(62965)
q=173: p=6619(880),205763(65416)
q=181: p=27091(6436)
q=193: p=43313(11221)
q=197: p=114487(34288),169097(52360)
q=211: p=432491(139381)
q=229: p=90709(25351)
q=233: p=92863(25906),283079(88690),2090131(690730)
q=257: p=65033(16195),2807087(928414)
q=277: p=28921(5116),7059077(2344531)
q=281: p=77849(19393),501967(158986)
q=293: p=4163681(1378420)
q=307: p=279707(83821)
q=317: p=13907(1360),42349(7882),99233(24730),298327(89404),1293797(420382),2090173(685735)
q=337: p=102337(24901),337367(101110)
q=347: p=5527(223),357787(107233)
q=349: p=3501781(1153882)
q=353: p=123209(30715)
q=397: p=468887(140548),781741(244171),5161697(1703230)
q=401: p=159209(39703)
q=421: p=55541(8971),743269(229513),24813749(8251603)
q=433: p=2019113(652831)
q=449: p=2088011(674302)
q=457: p=31745057(10558531)
q=467: p=6717143(2215075)
q=487: p=5421007(1781029)
q=499: p=2096851(672337),5833739(1917301)
q=509: p=35069(3376)
q=541: p=3201199(1035508)
q=547: p=54456047(18118831)
q=569: p=112967(19258)
q=593: p=241079(54070)
q=607: p=74426707(24768031)
q=613: p=19070279(6315280)
q=617: p=53507(5290)
q=641: p=6133867(1999966)
q=673: p=7664953(2505631)
q=677: p=20533141(6793831)
q=701: p=385597(90211),467101(115276)
q=709: p=29532511(9788632)
q=727: p=1578347(473287)
q=739: p=19036219(6285301)
q=751: p=141000259(46937503)
q=757: p=91957(9961),35958827(11922940)
q=761: p=576089(143833)
q=773: p=594449(148420),76782481(25527940)
q=787: p=1850267(554845)
q=797: p=20882497(6890962)
q=809: p=651257(162613),5867761(1885807),12388391(4058002)
q=827: p=96527(9571)
q=829: p=62189(4426)
q=853: p=108709(11215)
q=857: p=731033(182545)
q=877:p=327629(61267),546631(124036),2955653(906580),3831661(1197121),31863917(10536529),224585677(74776531)
q=881: p=53089(3013),772649(192943),113707591(37816486)
q=883: p=32524171(10755445)
q=907: p=18857647(6195787)
q=941: p=144311(15796),881729(220198)
q=947: p=56319607(18674083)
q=953: p=1282471(345850),143951131(47883010)
q=967: p=42746927(14145829),301098667(100262431)
q=977: p=398087(73750),950633(237415)
q=997: p=330010997(109893331)