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|00000510| 0a 20 20 20 4c 53 44 28 | 79 29 20 20 20 7c 7c 20 |.   LSD(|y)   || |
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|00000a40| 79 20 61 72 65 20 69 6e | 20 74 72 6f 75 62 6c 65 |y are in| trouble|
|00000a50| 20 69 66 20 6f 6e 65 20 | 6f 66 20 74 68 65 73 65 | if one |of these|
|00000a60| 20 74 77 6f 20 69 73 20 | 35 20 61 6e 64 20 74 68 | two is |5 and th|
|00000a70| 65 20 6f 74 68 65 72 20 | 69 73 20 65 76 65 6e 0a |e other |is even.|
|00000a80| 20 20 20 28 73 65 65 20 | 65 6e 74 72 69 65 73 20 |   (see |entries |
|00000a90| 6d 61 72 6b 65 64 20 77 | 69 74 68 20 2a 29 2e 20 |marked w|ith *). |
|00000aa0| 49 6e 20 74 68 69 73 20 | 63 61 73 65 20 77 65 20 |In this |case we |
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|00000ae0| 64 65 74 65 72 6d 69 6e | 20 74 68 65 20 6e 65 77 |determin| the new|
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|00000b00| 6c 74 20 77 68 69 63 68 | 20 69 73 3a 0a 0a 4e 6f |lt which| is:..No|
|00000b10| 74 65 20 68 6f 77 65 76 | 65 72 20 74 68 61 74 20 |te howev|er that |
|00000b20| 35 20 63 61 6e 6e 6f 74 | 20 62 65 20 60 67 65 6e |5 cannot| be `gen|
|00000b30| 65 72 61 74 65 64 27 20 | 66 72 6f 6d 20 6e 6f 6e |erated' |from non|
|00000b40| 20 35 2e 20 53 69 6d 69 | 6c 61 72 6c 79 20 65 76 | 5. Simi|larly ev|
|00000b50| 65 6e 0a 63 61 6e 6e 6f | 74 20 62 65 20 67 65 6e |en.canno|t be gen|
|00000b60| 65 72 61 74 65 64 20 66 | 72 6f 6d 20 6e 6f 6e 2d |erated f|rom non-|
|00000b70| 65 76 65 6e 2e 20 54 68 | 65 73 65 20 6d 69 67 68 |even. Th|ese migh|
|00000b80| 74 20 68 65 6c 70 20 69 | 6e 20 63 65 72 74 61 69 |t help i|n certai|
|00000b90| 6e 20 63 61 73 65 73 2e | 0a 0a 41 6c 73 6f 20 6e |n cases.|..Also n|
|00000ba0| 6f 74 65 20 74 68 61 74 | 20 69 6e 20 79 6f 75 72 |ote that| in your|
|00000bb0| 20 6e 6f 74 61 74 69 6f | 6e 0a 0a 4c 53 44 28 78 | notatio|n..LSD(x|
|00000bc0| 20 2a 20 35 29 20 3d 20 | 35 20 20 20 20 20 20 20 | * 5) = |5       |
|00000bd0| 20 20 69 66 20 4c 53 44 | 28 78 29 20 69 73 20 6f |  if LSD|(x) is o|
|00000be0| 64 64 0a 20 20 20 20 20 | 20 20 20 20 20 20 3d 20 |dd.     |      = |
|00000bf0| 4c 53 44 28 78 29 2f 32 | 20 20 69 66 20 4c 53 44 |LSD(x)/2|  if LSD|
|00000c00| 28 78 29 20 69 73 20 65 | 76 65 6e 2e 0a 0a 4e 6f |(x) is e|ven...No|
|00000c10| 77 2c 20 77 65 20 6e 65 | 76 65 72 20 77 61 6e 74 |w, we ne|ver want|
|00000c20| 20 74 6f 20 75 73 65 20 | 74 68 65 20 66 69 72 73 | to use |the firs|
|00000c30| 74 20 72 75 6c 65 3a 20 | 62 65 63 61 75 73 65 20 |t rule: |because |
|00000c40| 69 66 20 77 65 20 64 69 | 64 2c 20 77 65 20 77 6f |if we di|d, we wo|
|00000c50| 75 6c 64 0a 73 74 75 6d | 62 6c 65 20 6f 6e 20 74 |uld.stum|ble on t|
|00000c60| 68 65 20 66 61 63 74 20 | 4c 53 44 28 78 20 2a 20 |he fact |LSD(x * |
|00000c70| 65 76 65 6e 29 20 63 61 | 6e 6e 6f 74 20 62 65 20 |even) ca|nnot be |
|00000c80| 67 6f 74 20 66 72 6f 6d | 20 4c 53 44 28 78 29 20 |got from| LSD(x) |
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