26. (8分)定义:关于$x,y$的二元一次方程$ax + by = c$（其中$a≠b≠c≠0$）中的常数项$c$与未知数系数$a$互换,得到的方程叫“亲密方程”,例如:$ax + by = c$的“亲密方程”为$cx + by = a$.
(1)方程$x + 3y = 5$的“亲密方程”为________;
(2)已知关于$x,y$的二元一次方程$ax + by = c$的系数满足$a - 2b + c = 0$,且$ax + by = c$与它的“亲密方程”组成的方程组的解恰好是关于$x,y$的二元一次方程$mx + ny = p$的一个解,求代数$(m - 2n)m - p(p - 2n) + 2025$的值;
(3)已知整数$m,n,t$,满足条件$t ＜ n ＜ m$,并且$(4m - t)x + 2025y = m + 2t - 4$是关于$x,y$的二元一次方程$nx + 2025y = 3m + 4$的“亲密方程”,求$m$的值.

26. 【点拨】本题考查新定义,解二元一次方程组,解一元一次不等式组.
【解析】(1)$x +3y =5$ 的“亲密方程”为 $5x +3y =1$.
故答案为 $5x +3y =1$.
(2)$ax + by = c$ 的“亲密方程”为 $cx + by = a$,
$\therefore \begin{cases} ax + by = c,① \\ cx + by = a,② \end{cases}$ 的解满足方程 $mx + ny = p$.
$\because$ ① $-$ ②得 $(a -c)x = c -a$,$\therefore x = -1$,
$\therefore -a + by = c$,$\therefore by = a + c$.
$\because a -2b + c =0$,$\therefore 2b = a + c$,$\therefore by = 2b$,$\therefore y =2$,
$\therefore x = -1$,$y =2$ 是 $mx + ny = p$ 的一个解,
$\therefore -m +2n = p$,即 $m -2n = -p$,$p -2n = -m$,
$\therefore (m -2n)m -p(p -2n) +2\ 025 = -pm -p(-m) +2\ 025 =2\ 025$.
(3)$nx +2\ 025y =3m +4$ 的“亲密方程”是 $(3m +4)x +2\ 025y =n$.
由题意得 $4m -t =3m +4$,且 $m +2t -4 =n$,
化简得 $t =m -4$,$n =3m -12$.
$\because$ 整数 $m,n,t$ 满足条件 $t ＜ n ＜ m$,
$\therefore m -4 ＜3m -12 ＜m$,解得 $4 ＜ m ＜6$,$\therefore m =5$.