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求所有 x^2+y^2=5*z^2 ,正整數解

hint: (aa+bb) (cc+dd)=(ac+bd)^2+(ad-bc)^2

我覺得無解ㄝ∼

If set money again, it will be deleted

for aa+bb=cc, (a,c,b)=k,
a=k(pp-qq)
b=2kpq
c=k(pp+qq)
let z=c=k(pp+qq)
zz=kk((pp-qq)^2+(2pq)^2)
5=2*2+1*1
so,
5zz=kk(2*2+1*1)((pp-qq)^2+(2pq)^2)
=(2k(pp-qq)+k(2pq))^2 +(k(pp-qq)-2k(2pq))^2
=(2k(pp-qq)-k(2pq))^2 +(k(pp-qq)+2k(2pq))^2
=xx+yy

that is:
z=k(pp+qq)
{x,y}={2k|pp+pq-qq|,k|pp-4pq-qq|}
or ={k|pp-qq+4pq|,2k|pp-pq-qq|}

(p,q)=1, p>=q

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Ex:
when k=1,p=1, q=0 ==> z=1,{x,y}={2,1}
when k=1,p=1, q=1 ==> z=2,{x,y}={2,4}
when k=1,p=2, q=1 ==> z=5,{x,y}={10,5} or {11,2}
when k=1,p=3, q=1 ==> z=10,{x,y}={22,4} or {10,20}
when k=2,p=2, q=1 ==> z=10,{x,y}={22,4} or {10,20}
when k=1,p=4, q=1 ==> z=17,{x,y}={38,1}or {22,31}

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    請依法解 "[問題]某競賽題(2平方數平均等於另一平方數)"

嗚∼我猜錯了∼不過省了100元∼

今天我值班,四台刀,至少也有10000圓收入.這題想了2天的東西, 按照我的收費要20000圓,只收100是賠錢生意的.

四台刀?

it is discussion board, not set money is better

Meowth, you should set hint with all your questions  

  

出題者也可以領錢不是嗎？

forget 1000